Problem B. 4734. (October 2015)
B. 4734. Some fields (unit cubes) constituting a cubical lattice of edge 2015 units are infected by an unknown disease. The disease will spread if at least \(\displaystyle t\) fields in some row parallel to any edge of the cube are infected \(\displaystyle (1 \le t \le 2015)\). In that case, every field of that row will become infected in one minute. How many fields need to be infected initially in order to
\(\displaystyle a)\) make it possible
\(\displaystyle b)\) be certain
that the infection reaches all fields of the cube?
Proposed by G. Mészáros, Budapest
Deadline expired on November 10, 2015.
61 students sent a solution. 4 points: 12 students. 3 points: 10 students. 2 points: 14 students. 1 point: 15 students. 0 point: 8 students. Unfair, not evaluated: 2 solutionss.